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  • Presentation: 2017-05-30 13:15 Kappa, Västerås
    Ogutu, Carolyne
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    On Construction of Multinomial Lattices for Option Pricing2017Licentiate thesis, monograph (Other academic)
  • Presentation: 2017-05-31 13:15 Kappa, Västerås
    Musonda, John
    Mälardalen University, School of Education, Culture and Communication.
    Orthogonal Polynomials, Operators and Commutation Relations2017Licentiate thesis, monograph (Other academic)
    Abstract [en]

    Orthogonal polynomials, operators and commutation relations appear in many areas of mathematics, physics and engineering where they play a vital role. For instance, orthogonal functions in general are central to the development of Fourier series and wavelets which are essential to signal processing. In particular, as demonstrated in this thesis, orthogonal polynomials can be used to establish the L2-boundedness of singular integral operators which is a fundamental problem in harmonic analysis and a subject of extensive investigations. The Lp-convergence of Fourier series is closely related to the Lp-boundedness of singular integral operators. Many important relations in physical sciences are represented by operators satisfying various commutation relations. Such commutation relations play key roles in such areas as quantum mechanics, wavelet analysis, representation theory, spectral theory, and many others.

    This thesis consists of three main parts. The first part presents a new system of orthogonal polynomials, and establishes its relation to the previously studied systems in the class of Meixner–­Pollaczek polynomials. Boundedness properties of two singular integral operators of convolution type are investigated in the Hilbert spaces related to the relevant orthogonal polynomials. Orthogonal polynomials are used to prove boundedness in the weighted spaces and Fourier analysis is used to prove boundedness in the translation invariant case. It is proved in both cases that the two operators are bounded on L2-spaces, and estimates of the norms are obtained.

    The second part extends the investigation of the boundedness properties of the two singular integral operators to Lp-spaces on the real line, both in the weighted and unweighted spaces. It is proved that both operators are bounded on these spaces and estimates of the norms are obtained. This is achieved by first proving boundedness for L2 and weak boundedness for L1, and then using interpolation to obtain boundedness for the intermediate spaces. To obtain boundedness for the remaining spaces, duality is used in the translation invariant case, while the weighted case is partly based on the methods developed by M. Riesz in his paper of 1928 for the conjugate function operator.

    The third and final part derives simple and explicit formulas for reordering elements in an algebra with three generators and Lie type relations. Centralizers and centers are computed as an example of an application of the formulas.

  • Presentation: 2017-06-07 13:00 Gamma, Västerås
    Larsdotter Bodin, Ulrika
    Mälardalen University, School of Education, Culture and Communication.
    Förskollärares yrkeskunnande: Förskollärares erfarenheter av praktiskt handlande i pedagogisk verksamhet2017Licentiate thesis, monograph (Other academic)
    Abstract [en]

    The aim of this dissertation was to interpret and analyze how preschool teachers described their professional skills and to deepen understanding about this. Two questions were used to achieve this aim. The first question concerned what preschool teachers talked about regarding their experiences work in praxis. The second question concerned the manner in which preschool teachers' individual and collective reflection could contribute to new insights regarding their professional skills. Based on the three different forms of knowledge that Aristotle inspired: episteme, techne and fronesis skills can be said to consist of both theory and to a high degree, of practice in which the various forms both interact as complementary. Thus it is not enough merely to have scientific knowledge (episteme), or to know how something should be done only by general rules and principles (techne) to possess a skill. Rather professionalism is largely characterized by fronesis, a concept that can be translated as practical wisdom, and it cannot always be put into words. Dewey has highlighted the importance of reflection over every day conduct as an important tool to both broaden and alter the quality of practice work in praxis. In order to fulfill answer the aim of the dialogueseminar method was seen as a viable approach to collect empirical data. The emphasis of the method was to continuously reflect, both individually and in interaction with others and then share stories about their experience of practical work in praxis. The results showed that preschool teachers' professional skills emanated from their own life-world experience. Through this it was possible to focus and link practical action to two prominent themes. The themes were: expectations and approach and they describing the basis for the practical conduct preschool teachers related to and put into various concrete settings from the context they were operating in. Based on the study's second question, reflection was highlighted as both important and central to raising awareness of- and making new insights visible. According to preschool teachers, it had been enriching and energizing to be given opportunity to do this and the reafter to share their thoughts about their profession in dialogue. The results showed that preschool teachers' professional skills, with a focus on practical work, could both be widened and developed. Partly through individual reflection, but above all through collective reflection and conversations.